If a person walks at 4 mph, he covers a certain distance. If he walks at
9 mph, he covers 7.5 miles more. How much distance did he actually cover?
let the time be t hours
at 4 mph, the person covers 4t miles
at 9 mph, the person covers 9t miles
9t - 4t = 7.5
carry on ...
To find the distance the person actually covered, we can set up a system of equations based on the given information.
Let's assume that the distance covered by the person when walking at 4 mph is represented by 'd' (in miles).
Using the formula distance = speed × time, we can write the equation:
d = 4t, where 't' represents the time taken to cover the distance 'd'.
According to the second statement, if the person walks at 9 mph, they cover 7.5 miles more than the distance covered at 4 mph. Therefore, the distance covered at 9 mph can be represented as (d + 7.5).
Using the same formula, we can write the equation for the second scenario:
(d + 7.5) = 9t
Now we have a system of equations:
d = 4t
d + 7.5 = 9t
We can solve this system of equations to find the values of 'd' and 't'.
Rearranging the first equation, we get:
t = d/4
Substituting this value in the second equation, we have:
d + 7.5 = 9(d/4)
Simplifying this equation, we get:
4d + 30 = 9d
Moving all the terms involving 'd' to one side, we have:
9d - 4d = 30
Simplifying further, we get:
5d = 30
Dividing both sides by 5, the value of 'd' is:
d = 6
Therefore, the person actually covered a distance of 6 miles.